z-matrix errors occurred as the water molecule rotated. It can be said therefore that
direct protonation of B(OH) 4
− results in water elimination.
Four forms of hydrated boric acid with a water molecule hydrogen-bonded to the
boric acid were attempted (Fig. 3). To the naked C 3h structure, a water molecule
may only hydrogen bond in a donor-acceptor (DA) fashion (C 1 #2), whereas to the
naked C s #2 structure, a water molecule may hydrogen bond in either a double
donor (DD, C s #1 or C 1 #3), donor acceptor (DA, C 1 #1), or double acceptor (AA,
C s #2). All were energy minima, with the exception of C s #1 at the B3LYP/6-31G*
and all MP2 levels. These desymmetrized to C 1 #3, where the water is removed
from the BO 3 plane by varying amounts (significantly at the B3LYP and
MP2/6-31G* levels).
For the dihydrate, a C s and five C 1 forms were tried. The C 1 #4 and C 1 #5 forms
are derived from the naked C 3h structure and differ in the orientation of the free
hydrogen of the water molecules, either up,up (uu) or up,down (ud). The other
forms are derived from the naked C s #2 structure: namely, the C s/1 #1 (DD,AA), the
C 1 #2 (DD,DA), and the C 1 #3 (DA,AA). The C s form was stable at the HF,
C 3h
C 3v
C s #1
C s #2
C s
C
3
#
1 #1
Fig. 2 Structure of metaboric acid, [B 3 O 3 (OH) 3 ]
Table 7 Relative Energies of B 3 O 3 (OH) 3 (kJ/mol). c/v = excessive core-valence mixing
C 3h
C s #2
C s #1
C s #3
C 1 #1
C 3v
HF/6-31G*
0.0
4.0
40.0
38.7
41.4
123.9
HF/6-31+G*
0.0
3.9
39.0
37.7
40.3
120.8
HF/6-311+G*
0.0
4.0
39.7
38.3
41.0
122.9
B3LYP/6-31G*
0.0
3.7
40.9
39.5
42.1
126.7
B3LYP/6-31+G*
0.0
3.4
39.8
38.4
40.8
122.8
B3LYP/6-311+G*
0.0
3.6
40.0
38.6
41.1
122.3
MP2/6-31G*
0.0
4.0
43.4
41.9
44.7
134.4
MP2/6-31+G*
0.0
3.8
42.3
40.8
43.4
c/v
MP2/6-311+G*
0.0
3.9
43.2
41.7
44.4
An Ab Initio Study of Boric Acid, Borate …
155
direct protonation of B(OH) 4
− results in water elimination.
Four forms of hydrated boric acid with a water molecule hydrogen-bonded to the
boric acid were attempted (Fig. 3). To the naked C 3h structure, a water molecule
may only hydrogen bond in a donor-acceptor (DA) fashion (C 1 #2), whereas to the
naked C s #2 structure, a water molecule may hydrogen bond in either a double
donor (DD, C s #1 or C 1 #3), donor acceptor (DA, C 1 #1), or double acceptor (AA,
C s #2). All were energy minima, with the exception of C s #1 at the B3LYP/6-31G*
and all MP2 levels. These desymmetrized to C 1 #3, where the water is removed
from the BO 3 plane by varying amounts (significantly at the B3LYP and
MP2/6-31G* levels).
For the dihydrate, a C s and five C 1 forms were tried. The C 1 #4 and C 1 #5 forms
are derived from the naked C 3h structure and differ in the orientation of the free
hydrogen of the water molecules, either up,up (uu) or up,down (ud). The other
forms are derived from the naked C s #2 structure: namely, the C s/1 #1 (DD,AA), the
C 1 #2 (DD,DA), and the C 1 #3 (DA,AA). The C s form was stable at the HF,
C 3h
C 3v
C s #1
C s #2
C s
C
3
#
1 #1
Fig. 2 Structure of metaboric acid, [B 3 O 3 (OH) 3 ]
Table 7 Relative Energies of B 3 O 3 (OH) 3 (kJ/mol). c/v = excessive core-valence mixing
C 3h
C s #2
C s #1
C s #3
C 1 #1
C 3v
HF/6-31G*
0.0
4.0
40.0
38.7
41.4
123.9
HF/6-31+G*
0.0
3.9
39.0
37.7
40.3
120.8
HF/6-311+G*
0.0
4.0
39.7
38.3
41.0
122.9
B3LYP/6-31G*
0.0
3.7
40.9
39.5
42.1
126.7
B3LYP/6-31+G*
0.0
3.4
39.8
38.4
40.8
122.8
B3LYP/6-311+G*
0.0
3.6
40.0
38.6
41.1
122.3
MP2/6-31G*
0.0
4.0
43.4
41.9
44.7
134.4
MP2/6-31+G*
0.0
3.8
42.3
40.8
43.4
c/v
MP2/6-311+G*
0.0
3.9
43.2
41.7
44.4
An Ab Initio Study of Boric Acid, Borate …
155